EVENT DETAILS AND ABSTRACT

Title: Parameterizing degree n rational maps by multipliers of periodic orbits
Speaker: Igors Gorbovickis
Speaker Info: University of Toronto
Brief Description:
Special Note:
Abstract:

It was suggested by John Milnor to use the multipliers of the fixed points to parameterize the moduli space of degree 2 rational maps of the Riemann sphere. In this talk we will discuss an attempt to use multipliers of periodic orbits as the parameters on the moduli space of degree n polynomial or rational maps. We will show that at its generic point, the moduli space of degree n polynomial maps can be locally parameterized by the multipliers of n-1 arbitrary distinct periodic orbits. This is equivalent to the statement that these multipliers, considered as algebraic functions on the moduli space, are algebraically independent over the field of complex numbers. Further, we will discuss a generalization of the above result to the case of degree n rational maps.